Multi-channel sub-Nyquist cross-Spectral Estimation for Modal Analysis of Vibrating Structures

Operational modal analysis (OMA) is a widely used construction verification and structural health monitoring technique aiming to obtain the modal properties of vibrating civil engineering structures subject to ambient dynamic loads by collecting and processing structural response acceleration signals. Motivated by the need for cost-efficient OMA using wireless sensor networks which acquire and transmit measurements at a lower than the Nyquist rate, a novel OMA approach is put forth to derive modal properties directly from sub-Nyquist sampled (compressed) acceleration measurements from arrays of sensors. This is achieved by adopting sub-Nyquist deterministic non-uniform multi-coset sampling devices and by extending a previously proposed in the literature power spectrum blind sampling (PSBS) method for single-channel spectral estimation of stochastic processes to treat the case of multiple channel cross-spectral estimation. The standard frequency domain decomposition is used to obtain the modal properties from the cross-spectral matrix derived directly from the sub-Nyquist measurements. The applicability and efficiency of the proposed approach is exemplified by retrieving mode shapes of a white-noise excited simply supported steel beam with good accuracy according to the widely used modal assurance criterion (MAC) using 70% less than the Nyquist rate measurements

Vibration-based structural performance assessment via output-only sub-Nyquist/compressive wireless sensor data

This paper assesses two different approaches for efficient output - only Vibration - based Structural Health Monitoring (V - SHM) in large - scale civil engineering structures, promoting the use of dense arrays of low - power wireless sensors. Firstly, a non - uniform deterministic sub - Nyquist multi - coset sampling scheme is considered to acquire ambient stationary structural response signals. This sampling scheme is coupled with a power spectrum blind sampling technique along with the frequency domain decomposition algorithm of operational modal analysis to obtain structural modal properties. This is accomplished without necessitating either signal reconstruction in the time - domain or signal sparsity assumption . Secondly, a spectro-temporal compressive sensing approach is considered applicable to cases where sign al reconstruction in time - domain is desired. The latter approach considers non-uniform in time random sampling at sub - Nyquist average rates informed by prior knowledge of signal sparsity gained through smart on-sensor operations and sensor/server communication. The usefulness and applicability of two approaches is numerically demonstrated by considering field recorded data pertaining to the monitoring of an overpass open to the traffic and of an operating on-shore wind turbine

Sub-Nyquist signal-reconstruction-free operational modal analysis and damage detection in the presence of noise

Motivated by a need to reduce energy consumption in wireless sensors for vibration-based structural health monitoring (SHM) associated with data acquisition and transmission, this paper puts forth a novel approach for undertaking operational modal analysis (OMA) and damage localization relying on compressed vibrations measurements sampled at rates well below the Nyquist rate. Specifically, non-uniform deterministic sub-Nyquist multi-coset sampling of response acceleration signals in white noise excited linear structures is considered in conjunction with a power spectrum blind sampling/estimation technique which retrieves/samples the power spectral density matrix from arrays of sensors directly from the sub-Nyquist measurements (i.e., in the compressed domain) without signal reconstruction in the time-domain and without posing any signal sparsity conditions. The frequency domain decomposition algorithm is then applied to the power spectral density matrix to extract natural frequencies and mode shapes as a standard OMA step. Further, the modal strain energy index (MSEI) is considered for damage localization based on the mode shapes extracted directly from the compressed measurements. The effectiveness and accuracy of the proposed approach is numerically assessed by considering simulated vibration data pertaining to a white-noise excited simply supported beam in healthy and in 3 damaged states, contaminated with Gaussian white noise. Good accuracy is achieved in estimating mode shapes (quantified in terms of the modal assurance criterion) and natural frequencies from an array of 15 multi-coset devices sampling at a 70% slower than the Nyquist frequency rate for SNRs as low as 10db. Damage localization of equal level/quality is also achieved by the MSEI applied to mode shapes derived from noisy sub-Nyquist (70% compression) and Nyquist measurements for all damaged states considered. Overall, the furnished numerical results demonstrate that the herein considered sub-Nyquist sampling and multi-sensor power spectral density estimation techniques coupled with standard OMA and damage detection approaches can achieve effective SHM from significantly fewer noisy acceleration measurements

Compressive power spectrum sensing for vibration-based output-only system identification of structural systems in the presence of noise

Motivated by the need to reduce monetary and energy consumption costs of wireless sensor networks in undertaking output-only/operational modal analysis of engineering structures, this paper considers a multi-coset analog-toinformation converter for structural system identification from acceleration response signals of white noise excited linear damped structures sampled at sub-Nyquist rates. The underlying natural frequencies, peak gains in the frequency domain, and critical damping ratios of the vibrating structures are estimated directly from the sub-Nyquist measurements and, therefore, the computationally demanding signal reconstruction step is by-passed. This is accomplished by first employing a power spectrum blind sampling (PSBS) technique for multi-band wide sense stationary stochastic processes in conjunction with deterministic non-uniform multi-coset sampling patterns derived from solving a weighted least square optimization problem. Next, modal properties are derived by the standard frequency domain peak picking algorithm. Special attention is focused on assessing the potential of the adopted PSBS technique, which poses no sparsity requirements to the sensed signals, to derive accurate estimates of modal structural system properties from noisy sub- Nyquist measurements. To this aim, sub-Nyquist sampled acceleration response signals corrupted by various levels of additive white noise pertaining to a benchmark space truss structure with closely spaced natural frequencies are obtained within an efficient Monte Carlo simulation-based framework. Accurate estimates of natural frequencies and reasonable estimates of local peak spectral ordinates and critical damping ratios are derived from measurements sampled at about 70% below the Nyquist rate and for SNR as low as 0db demonstrating that the adopted approach enjoys noise immunity

Compressive sensing spectral estimation for output-only structural system identification

In this paper a compressive sensing (CS), sub-Nyquist, non-uniform deterministic sampling technique is considered in conjunction with a computationally efficient power spectrum estimation approach for frequency domain output-only system identification of linear white noise excited structural systems. The adopted CS sensing spectral estimation approach assumes multi-band input random signals/stochastic processes without posing any signal sparsity requirements and therefore it is applicable to linear structures with arbitrary number of degrees of freedom and level of damping. Further, it applies directly to the sub-Nyquist (CS) measurements and, thus, it by-passes the computationally demanding signal reconstruction step from CS measurements. Numerical results pertaining to the acceleration response of a damped structure with closely-spaced natural frequencies are provided to demonstrate the effectiveness of the considered approach to provide reliable estimates of natural frequencies by means of the standard frequency domain peak-picking algorithm of operational modal analysis using up to 90% fewer measurements compared to the Nyquist rate sampled data. It is envisioned that this study will further familiarize the structural dynamics community with the potential of CS-based techniques for vibration-based structural health monitoring and condition assessment of engineering structures

Assessment of sub-Nyquist deterministic and random data sampling techniques for operational modal analysis

This paper assesses numerically the potential of two different spectral estimation approaches supporting non-uniform in time data sampling at sub-Nyquist average rates (i.e., below the Nyquist frequency) to reduce data transmission payloads in wireless sensor networks (WSNs) for operational modal analysis (OMA) of civil engineering structures. This consideration relaxes transmission bandwidth constraints in WSNs and prolongs sensor battery life since wireless transmission is the most energy-hungry on-sensor operation. Both the approaches assume acquisition of sub-Nyquist structural response acceleration measurements and transmission to a base station without on-sensor processing. The response acceleration power spectral density matrix is estimated directly from the sub-Nyquist measurements and structural mode shapes are extracted using the frequency domain decomposition algorithm. The first approach relies on the compressive sensing (CS) theory to treat sub-Nyquist randomly sampled data assuming that the acceleration signals are sparse/compressible in the frequency domain (i.e., have a small number of Fourier coefficients with significant magnitude). The second approach is based on a power spectrum blind sampling (PSBS) technique considering periodic deterministic sub-Nyquist “multi-coset” sampling and treating the acceleration signals as wide-sense stationary stochastic processes without posing any sparsity conditions. The modal assurance criterion (MAC) is adopted to quantify the quality of mode shapes derived by the two approaches at different sub-Nyquist compression rates (CRs) using computer-generated signals of different sparsity and field-recorded stationary data pertaining to an overpass in Zurich, Switzerland. It is shown that for a given CR, the performance of the CS-based approach is detrimentally affected by signal sparsity, while the PSBS-based approach achieves MAC>0.96 independently of signal sparsity for CRs as low as 11% the Nyquist rate. It is concluded that the PSBS-based approach reduces effectively data transmission requirements in WSNs for OMA, without being limited by signal sparsity and without requiring a priori assumptions or knowledge of signal sparsity

A multi-sensor sub-Nyquist power spectrum blind sampling approach for low-power wireless sensors in operational modal analysis applications

A novel multi-sensor power spectrum blind sampling (PSBS) approach is proposed supporting low-power wireless sensor networks (WSN) for Operational Modal Analysis (OMA) applications. The developed approach relies on arrays of wireless sensors, employing deterministic non-uniform in time multi-coset sampling to acquire structural response acceleration signals at sub-Nyquist sampling rates, treated as realizations of stationary random processes without making any assumption about the average signal frequency content and spectral support. The acquired compressed measurements are transmitted to a central server and collectively processed via a PSBS technique, herein extended to the multi-sensor case, to estimate the power spectral density matrix of an underlying spatially correlated stationary response acceleration random process directly from the compressed measurements. Structural modal properties are then extracted through standard frequency domain decomposition (FDD). The efficacy of the proposed approach to resolve closely-spaced modes is numerically tested for various data compression levels using noisy response acceleration signals of a white-noise excited finite element model of a space truss as well as field-recorded acceleration time-histories of an instrumented bridge under operational loading. It is shown that accurate mode shapes based on the modal assurance criterion can be obtained from as low as 89% less measurements compared to conventional non-compressive FDD at Nyquist sampling rate. Further, significant gains in energy consumption and battery lifetime prolongation of the order of years are estimated, assuming wireless sensors operating on multi-coset sampling at different data compression levels. It is, therefore, concluded that the proposed PSBS approach could provide long-term structural health monitoring systems with low-maintenance cost once wireless sensors with multi-coset sampling capabilities become commercially available

Compressive techniques for sub-Nyquist data acquisition & processing in vibration-based structural health monitoring of engineering structures

Vibration-based structural health monitoring (VSHM) is an automated method for assessing the integrity and performance of dynamically excited structures through processing of structural vibration response signals acquired by arrays of sensors. From a technological viewpoint, wireless sensor networks (WSNs) offer less obtrusive, more economical, and rapid VSHM deployments in civil structures compared to their tethered counterparts, especially in monitoring large-scale and geometrically complex structures. However, WSNs are constrained by certain practical issues related to local power supply at sensors and restrictions to the amount of wirelessly transmitted data due to increased power consumptions and bandwidth limitations in wireless communications. The primary objective of this thesis is to resolve the above issues by considering sub-Nyquist data acquisition and processing techniques that involve simultaneous signal acquisition and compression before transmission. This drastically reduces the sampling and transmission requirements leading to reduced power consumptions up to 85-90% compared to conventional approaches at Nyquist rate. Within this context, the current state-of-the-art VSHM approaches exploits the theory of compressive sensing (CS) to acquire structural responses at non-uniform random sub-Nyquist sampling schemes. By exploiting the sparse structure of the analysed signals in a known vector basis (i.e., non-zero signal coefficients), the original time-domain signals are reconstructed at the uniform Nyquist grid by solving an underdetermined optimisation problem subject to signal sparsity constraints. However, the CS sparse recovery is a computationally intensive problem that strongly depends on and is limited by the sparsity attributes of the measured signals on a pre-defined expansion basis. This sparsity information, though, is unknown in real-time VSHM deployments while it is adversely affected by noisy environments encountered in practice. To efficiently address the above limitations encountered in CS-based VSHM methods, this research study proposes three alternative approaches for energy-efficient VSHM using compressed structural response signals under ambient vibrations. The first approach aims to enhance the sparsity information of vibrating structural responses by considering their representation on the wavelet transform domain using various oscillatory functions with different frequency domain attributes. In this respect, a novel data-driven damage detection algorithm is developed herein, emerged as a fusion of the CS framework with the Relative Wavelet Entropy (RWE) damage index. By processing sparse signal coefficients on the harmonic wavelet transform for two comparative structural states (i.e., damage versus healthy state), CS-based RWE damage indices are retrieved from a significantly reduced number of wavelet coefficients without reconstructing structural responses in time-domain. The second approach involves a novel signal-agnostic sub-Nyquist spectral estimation method free from sparsity constraints, which is proposed herein as a viable alternative for power-efficient WSNs in VSHM applications. The developed method relies on Power Spectrum Blind Sampling (PSBS) techniques together with a deterministic multi-coset sampling pattern, capable to acquire stationary structural responses at sub-Nyquist rates without imposing sparsity conditions. Based on a network of wireless sensors operating on the same sampling pattern, auto/cross power-spectral density estimates are computed directly from compressed data by solving an overdetermined optimisation problem; thus, by-passing the computationally intensive signal reconstruction operations in time-domain. This innovative approach can be fused with standard operational modal analysis algorithms to estimate the inherent resonant frequencies and modal deflected shapes of structures under low-amplitude ambient vibrations with the minimum power, computational and memory requirements at the sensor, while outperforming pertinent CS-based approaches. Based on the extracted modal in formation, numerous data-driven damage detection strategies can be further employed to evaluate the condition of the monitored structures. The third approach of this thesis proposes a noise-immune damage detection method capable to capture small shifts in structural natural frequencies before and after a seismic event of low intensity using compressed acceleration data contaminated with broadband noise. This novel approach relies on a recently established sub-Nyquist pseudo-spectral estimation method which combines the deterministic co-prime sub-Nyquist sampling technique with the multiple signal classification (MUSIC) pseudo-spectrum estimator. This is also a signal-agnostic and signal reconstruction-free method that treats structural response signals as wide-sense stationary stochastic processes to retrieve, with very high resolution, auto-power spectral densities and structural natural frequency estimates directly from compressed data while filtering out additive broadband noise